Single molecule (SM) measurements are rapidly becoming commonplace in research laboratories around the world and are contributing to many areas of investigation because of their ability to provide insight into phenomena that were previously intractable because of the ensemble averaging present in bulk measurements. In particular the dynamics of conformationally heterogeneous systems are benefiting from single-molecule studies. Protein folding and conformational dynamics, enzymology, ribozyme function, bacterial light harvesting, and protein-nucleic acid interactions are just a few examples of complex systems that have benefited from the application of SM techniques. However, the impact of SM results has been mitigated by the lack of uniform data analysis and interpretation. The proposed research focuses on SM fluorescence measurements and how to place the experimental design, analysis, and expectations onto solid statistical and theoretical ground. Three specific aims are proposed: 1. Use information theory to determine the fundamental limits of SM experiments. 2. Develop statistically rigorous analysis methods based on hidden Markov models. 3. Implement methods as user-oriented additions to common data analysis packages. The significance to health of this research is through its contribution to the many ongoing SM investigations into biological systems. SM measurements are revolutionizing our approach to many problems in chemical biology, yet they are still being interpreted and designed based on assumptions that are only valid for ensemble measurements of bulk samples. This can result in collection of data that cannot be adequately interpreted using traditional methods. A consistent theoretical framework for SM measurements would be a significant step forward for the field. Aim 1 will provide a theoretical framework that can be used for experimental design as it provides the limit of the measurement's ability to make inferences about the properties of the system. It will also provide the benchmark (the Cram[unreadable]r-Rao bound) by which to judge data reduction methods. Aim 2 develops the algorithms and core codes to implement statistically rigorous methods of data analysis that allow unbiased estimation of system parameters with accuracy approaching the Cram[unreadable]r-Rao bound including meaning uncertainty estimates. Aim 3 provides useable tools for experimental design and analysis to allow other investigators to exploit these methods for their own research.